Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials within the quantum concept. Phys. Rev. 115, 485–491 (1959).
Klitzing, Ok. V., Dorda, G. & Pepper, M. New methodology for high-accuracy willpower of the fine-structure fixed based mostly on quantized Corridor resistance. Phys. Rev. Lett. 45, 494–497 (1980).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Moore, J. E. The beginning of topological insulators. Nature 464, 194–198 (2010).
Tan, X. et al. Topological Maxwell metallic bands in a superconducting qutrit. Phys. Rev. Lett. 120, 130503 (2018).
Chen, M. et al. An artificial monopole supply of Kalb-Ramond discipline in diamond. Science 375, 1017–1020 (2022).
Sugawa, S., Salces-Carcoba, F., Perry, A. R., Yue, Y. & Spielman, I. B. Second Chern variety of a quantum-simulated non-abelian Yang monopole. Science 360, 1429–1434 (2018).
Guo, Q. et al. Experimental statement of non-Abelian topological expenses and edge states. Nature 594, 195–200 (2021).
Wu, Q., Soluyanov, A. A. & Bzdušek, T. Non-Abelian band topology in noninteracting metals. Science 365, 1273–1277 (2019).
Jiang, B. et al. Experimental statement of non-Abelian topological acoustic semimetals and their section transitions. Nat. Phys. 17, 1239–1246 (2021).
Bouhon, A. et al. Non-Abelian reciprocal braiding of Weyl factors and its manifestation in ZrTe. Nat. Phys. 16, 1137–1143 (2020).
Ünal, F. N., Bouhon, A. & Slager, R.-J. Topological Euler class as a dynamical observable in optical lattices. Phys. Rev. Lett. 125, 053601 (2020).
Slager, R. J., Bouhon, A. & Ünal, F. N. Non-Abelian Floquet braiding and anomalous Dirac string section in periodically pushed techniques. Nat. Commun. 15, 1144 (2024).
Kruthoff, J. et al. Topological classification of crystalline insulators via band construction combinatorics. Phys. Rev. X 7, 041069 (2017).
Kitaev, A. Periodic desk for topological insulators and superconductors. AIP Conf. Proc. 1134, 22–30 (2009).
Ryu, S., Schnyder, A. P., Furusaki, A. & Ludwig, A. W. W. Topological insulators and superconductors: tenfold method and dimensional hierarchy. New J. Phys. 12, 065010 (2010).
Berry, M. Physics of nonhermitian degeneracies. Czechoslov. J. Phys. 54, 1039–1047 (2004).
Heiss, W. D. The physics of remarkable factors. J. Phys. A Math. Theor. 45, 444016 (2012).
Bergholtz, E. J., Budich, J. C. & Kunst, F. Ok. Distinctive topology of non-Hermitian techniques. Rev. Mod. Phys. 93, 015005 (2021).
Ding, Ok., Fang, C. & Ma, G. Non-Hermitian topology and exceptional-point geometries. Nat. Rev. Phys. 4, 745–760 (2022).
Hu, H. & Zhao, E. Knots and non-Hermitian Bloch bands. Phys. Rev. Lett. 126, 010401 (2021).
Shen, H., Zhen, B. & Fu, L. Topological band concept for non-Hermitian Hamiltonians. Phys. Rev. Lett. 120, 146402 (2018).
Gong, Z. Y. et al. Topological phases of non-Hermitian techniques. Phys. Rev. X 8, 031079 (2018).
Kawabata, Ok., Bessho, T. & Sato, M. Classification of remarkable factors and non-Hermitian topological semimetals. Phys. Rev. Lett. 123, 066405 (2019).
Kawabata, Ok., Shiozaki, Ok., Ueda, M. & Sato, M. Symmetry and topology in non-Hermitian physics. Phys. Rev. X 9, 041015 (2019).
Zhang, W. et al. Commentary of non-Hermitian topology with nonunitary dynamics of strong state spins. Phys. Rev. Lett. 127, 090501 (2021).
König, J. L. Ok., Yang, Ok., Budich, J. C. & Bergholtz, E. J. Braid-protected topological band buildings with unpaired distinctive factors. Phys. Rev. Res. 5, L042010 (2023).
Feng, L., Wong, Z. J., Ma, R.-M., Wang, Y. & Zhang, X. Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014).
Hodaei, H., Miri, M.-A., Heinrich, M., Christodoulides, D. N. & Khajavikhan, M. Parity-time-symmetric microring lasers. Science 346, 975–978 (2014).
Chen, W., Özdemir, Ş. Ok., Zhao, G., Wiersig, J. & Yang, L. Distinctive factors improve sensing in an optical microcavity. Nature 548, 192–196 (2017).
Hokmabadi, M. P., Schumer, A., Christodoulides, D. N. & Khajavikhan, M. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature 576, 70–74 (2019).
Gong, Z., Bello, M., Malz, D. & Kunst, F. Ok. Anomalous behaviors of quantum emitters in non-Hermitian baths. Phys. Rev. Lett. 129, 223601 (2022).
Cao, W. et al. Reservoir-mediated quantum correlations in non-Hermitian optical system. Phys. Rev. Lett. 124, 030401 (2020).
Regensburger, A. et al. Parity-time artificial photonic lattices. Nature 488, 167–171 (2012).
Lin, Z. et al. Unidirectional invisibility induced by PT-symmetric periodic buildings. Phys. Rev. Lett. 106, 213901 (2011).
Doppler, J. et al. Dynamically encircling an distinctive level for uneven mode switching. Nature 537, 76–79 (2016).
Hassan, A. U., Zhen, B., Soljačić, M., Khajavikhan, M. & Christodoulides, D. N. Dynamically encircling distinctive factors: actual evolution and polarization state conversion. Phys. Rev. Lett. 118, 093002 (2017).
Liu, W., Wu, Y., Duan, C.-Ok., Rong, X. & Du, J. Dynamically encircling an distinctive level in an actual quantum system. Phys. Rev. Lett. 126, 170506 (2021).
Wang, Ok., Dutt, A., Wojcik, C. C. & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 598, 59–64 (2021).
Patil, Y. S. S. et al. Measuring the knot of non-Hermitian degeneracies and non-commuting braids. Nature 607, 271–275 (2022).
Li, Z. & Mong, R. S. Ok. Homotopical characterization of non-Hermitian band buildings. Phys. Rev. B 103, 155129 (2021).
Dai, T. et al. Non-Hermitian topological section transitions managed by nonlinearity. Nat. Phys. 20, 101–108 (2024).
Guo, C.-X., Chen, S., Ding, Ok. & Hu, H. Distinctive non-Abelian topology in multiband non-Hermitian techniques. Phys. Rev. Lett. 130, 157201 (2023).
Hu, H., Solar, S. & Chen, S. Knot topology of remarkable level and non-Hermitian no-go theorem. Phys. Rev. Res. 4, L022064 (2022).
Li, Z.-J., Cardoso, G., Bergholtz, E. J. & Jiang, Q.-D. Braids and higher-order distinctive factors from the interaction between lossy defects and topological boundary states. Phys. Rev. Res. 6, 043023 (2024).
Arkhipov, I. I., Miranowicz, A., Minganti, F., Özdemir, Ş. Ok. & Nori, F. Dynamically crossing diabolic factors whereas encircling distinctive curves: a programmable symmetric-asymmetric multimode change. Nat. Commun. 14, 2076 (2023).
Borgnia, D. S., Kruchkov, A. J. & Slager, R.-J. Non-Hermitian boundary modes and topology. Phys. Rev. Lett. 124, 056802 (2020).
Yang, Z., Schnyder, A. P., Hu, J. & Chiu, C.-Ok. Fermion doubling theorems in two-dimensional non-Hermitian techniques for Fermi factors and distinctive factors. Phys. Rev. Lett. 126, 086401 (2021).
Wojcik, C. C., Solar, X.-Q., Bzdušek, T. & Fan, S. Homotopy characterization of non-Hermitian Hamiltonians. Phys. Rev. B 101, 205417 (2020).
Wu, Y. et al. Commentary of parity-time symmetry breaking in a single-spin system. Science 346, 878–880 (2019).
Wu, Y. et al. Third-order distinctive line in a nitrogen-vacancy spin system. Nat. Nanotechnol. 19, 160–165 (2024).
Tang, W., Ding, Ok. & Ma, G. Direct measurement of topological properties of an distinctive parabola. Phys. Rev. Lett. 127, 034301 (2021).
Zhang, R. Y. et al. Symmetry-protected topological distinctive chains in non-Hermitian crystals. Commun. Phys. 6, 169 (2023).
Bouhon, A., Bzdušek, T. & Slager, R.-J. Geometric strategy to fragile topology past symmetry indicators. Phys. Rev. B 102, 115135 (2020).
Zhong, J., Wojcik, C. C., Cheng, D. & Fan, S. Numerical and theoretical research of eigenenergy braids in two-dimensional photonic crystals. Phys. Rev. B 108, 195413 (2023).
Solar, Y. et al. Fractional quantum Zeno impact rising from non-Hermitian physics. Phys. Rev. X 13, 031009 (2023).
Solar, Ok. & Yi, W. Encircling the Liouvillian distinctive factors: a short overview. AAPPS Bull. 34, 22 (2024).
Pavlov, A. I., Gefen, Y. & Shnirman, A. Topological transitions in quantum leap dynamics: hidden distinctive factors. Phys. Rev. B 111, 104301 (2025).